Electromechanical Analysis of a Ring-type Piezoelectric Transformer

The idea of a piezoelectric transformer (PT) was first implemented by Rosen (Rosen, 1956), as shown in Fig.1. It used the coupling effect between electrical and mechanical energy of piezoelectric materials. A sinusoidal signal is used to excite mechanical vibrations by the inverse piezoelectric effect via the driver section. An output voltage can be induced in the generator part due to the direct piezoelectric effect. The PT offers many advantages over the conventional electromagnetic transformer such as high power-to-volume ratio, electromagnetic field immunity, and nonflammable. Due to the demand on miniaturization of power supplying systems of electrical equipment, the study of PT has become a very active research area in engineering. In literatures (Sasaki, 1993; Bishop, 1998), many piezoelectric transformers have been proposed and a few of them found practical applications. Apart from switching power supply system, a Roson-type PT has been adopted in cold cathode fluorescent lamp inverters for liquid-crystal display. The PT with multilayer structure to provide high-output power may be used in various kinds of power supply units. Recently, PT of ring (Hu, 2001) or disk (Laoratanakul, 2002) shapes have been proposed and investigated. Their main advantages are simple structure and small size. In comparing with the structure of a ring and a disk, the PZT ring offers higher electromechanical coupling implies that a ring structure is more efficient in converting mechanical energy to electrical energy, and vice versa, which is essential for a high performance PT. Different from all the conventional PT, the ring-type PT requires only a single poling process and a proper electrode pattern, and it was fabricated by a PZT ring by dividing one of the electrodes into two concentric circular regions. Because of the mode coupling effect and the complexity of vibration modes at high frequency, the conventional lumped-equivalent circuit method may not accurately predict the dynamic behaviors of the PT. In this chapter, an electromechanical model for a ring-type PT is obtained based on Hamilton’s principle. In order to establish the model, vibration characteristics of the piezoelectric ring with free boundary conditions are analyzed in advance, and the natural frequencies and mode shapes are obtained. In addition, an equivalent circuit model of the PT is obtained based on the equations of the motion for the coupling electromechanical system. Furthermore, the voltage step-up ratio, input impedance, output impedance, input 1